Kinetic to Elastic Potential Energy

[logan3]

Homework Statement

A moving car has 40,000 J of kinetic energy while moving at a speed of 7.0 m/s. A spring-loaded automobile bumper compresses 0.30 m when the car hits a wall and stops. What can you learn about the bumper’s spring using this information? Answer quantitatively and list the assumptions that you made.

[itex]KE = 40,000 J[/itex]
[itex]v_i = 7.0 m/s[/itex]
[itex]v_f = 0 m/s[/itex]
[itex]\vec s = 0.30 m[/itex]

Homework Equations

[itex]KE = Elastic PE = \frac {1}{2} k {\vec s}^2 \Rightarrow k = \frac {2KE}{{\vec s}^2}[/itex]

The Attempt at a Solution

[itex]k = \frac {2(40,000 J)}{(0.30 m)^2} = 888888.88 N/m \sim 8.9x10^5 N/m[/itex]

I learned that the bumper's spring has a constant of 8.9x10^5 N/m. I assumed that energy wasn't lost from the point when the car had 40,000 J of KE to when it impacted the wall, i.e. the energy was perfectly conserved.

Thank-you

 

[haruspex]

Looks ok. Not sure it is necessary to require that work is perfectly conserved, nor is it the time up to the impact that's of interest. Even if the spring failed to re-expand when released, the answer would be the same. Might be more relevant to mention that you assume there are no compressions anywhere else in the system (car or wall) during the impact.

 

[logan3]

Thank-you haruspex.